A projectile is thrown upward so that its distance above the ground after t seconds is h(t)=-16t^2 + 570t. After how many seconds does it reach its maximum​ height?

Answer 1

570 feet/second ????
You threw it up at about 400 miles per hour, typo but anyway

where is the vertex of that parabola?
16 t^2 -570 t = -h

t^2 - 265/8 t +265^2/16^2 = -h+265^2/16^2

(t-265/16)^2 = etc
so vertex at t = 265/16
BUT
I do not believe you

Answer 2

vertex at t = -b/2a = 570/32 = 285/16